Stochastic source seeking with tuning of forward velocity

Using the method of stochastic extremum seeking, we navigate an autonomous vehicle, modeled as a nonholonomic unicycle, towards the maximum of an unknown, spatially distributed signal field by measuring only the signal at the vehicle´s position. The vehicle position is not measured. Keeping the angular velocity constant, we control the forward velocity by designing a stochastic source seeking control law, which employs excitation based on filtered white noise rather than sinusoidal perturbations used in previous works. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source and provide numerical simulations to illustrate the effectiveness of the algorithm.